Breaking Mechanical Holography in Combinatorial Metamaterials
arXiv:2411.15760 · doi:10.1103/wtgy-8fx1
Abstract
Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response strongly depends on the mutual orientations of the blocks within the lattice. We study a family of possible block types for the square, honeycomb, and cubic lattices. Blocks that are centrally symmetric induce holographic order, such that mechanical compatibility (meaning that blocks do not impede each other's motion) implies bulk-boundary coupling. With them, one can design a compatible metamaterial that will deform in any desired texture only on part of its boundary. With blocks that break holographic order, we demonstrate how to design the deformation texture on the entire boundary. Correspondingly, the number of compatible holographic metamaterials scales exponentially with the boundary, while in non-holographic cases we show that it scales exponentially with the bulk.
See accompanying paper: Defect Positioning in Combinatorial Metamaterials arXiv:2412.01227
References in corpus (21)
- Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
- Colloquium: Artificial spin ice: Designing and imaging magnetic frustration
- Combinatorial Design of Textured Mechanical Metamaterials
- Nonlinear conduction via solitons in a topological mechanical insulator
- Realizing Colloidal Artificial Ice on Arrays of Optical Traps
- Unhappy Vertices in Artificial Spin Ice: Degeneracy from Vertex-Frustration
- Engineering of frustration in colloidal artificial ices realized on microfeatured grooved lattices
- Dualities and non-Abelian mechanics
- Counting and Sequential Information Processing in Mechanical Metamaterials
- Topological defects produce exotic mechanics in complex metamaterials
- Conformal Elasticity of Mechanism-Based Metamaterials
- Emergent Disorder and Mechanical Memory in Periodic Metamaterials
- Geometric charges and nonlinear elasticity of soft metamaterials
- Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
- Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials
- Design of pseudo-mechanisms and multistable units for mechanical metamaterials
- Response evolution of mechanical metamaterials under architectural transformations
- Topologically Protected Steady Cycles in an Ice-Like Mechanical Metamaterial
- Topology Restricts Quasidegeneracy in Sheared Square Colloidal Ice
- Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration
- Emergent Nonlocal Combinatorial Design Rules for Multimodal Metamaterials